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Choix de partenaires en p2p suivant des critères de
disponibilité
Stevens Le Blond, Fabrice Le Fessant, Erwan Le Merrer
To cite this version:
Stevens Le Blond, Fabrice Le Fessant, Erwan Le Merrer. Choix de partenaires en p2p suivant des
critères de disponibilité. conférence francaise sur les systèmes d’exploitation, Sep 2009, Toulouse,
France. �inria-00432747�
Toulouse,Fran e, du 9au11 septembre 2009
Choix de partenaires en P2P suivant des ritères de disponibilité StevensLe Blond,Fabri e Le Fessant,ErwanLe Merrer
INRIA Sophia-Antipolis/INRIASa lay/INRIARennes
{Stevens.Le-Blond,Fabri e.Le-Fessant,Er wan .Le- Merrer} inria .fr
Résumé
Nous étudions la problématique de re her he distribuée de pairs orrespondant à un motif de disponibilitédonné,dansunsystèmepair-à-pair(P2P).Motivéspar desexemples on rets, nous spé i ons deux problèmes formelsde orrespondan e de disponibilité quiapparaissent dans des appli ationsréelles: la orrespondan ededé onnexion,oùlespairs her hentdespartenairesdont ladé onnexion oïn ideave laleur,etla orrespondan e deprésen e,où lespairs her hent des partenaires onne tés en même temps qu'eux dans le futur. Nous proposons, omme solution peu oûteuse etpassant àl'é helle, l'utilisation deproto oles épidémiques pour lagestion de la topologieduréseau logique( ommeleproto oleT-Man);desmétriques adéquatessont fournies pour les deux problèmes de orrespondan e. Notre solution a été évaluée en simulant deux appli ations P2P, l'ordonnan ement de tâ hes et le sto kage de hiers, sur une tra e inédite d'eDonkey,laplusgrandefournissantlesinformations dedisponibilitédespairs. Nousprouvons toutd'abord l'existen ede motifsréguliersdanslessessionsde 14Mde pairssur27 jours. Nous montrons également, en utilisant 7 joursd'historique, qu'unprédi teur simple peutséle tionner despairsprédi tibles,pour prédireave su èsleurpériodedeprésen eenligne pour lasemaine suivante. En n, les simulations ont montré que notre solution simple a fourni rapidement de bons partenaires a n de répondre au besoin des deux appli ations, et ainsi de leur permettre de s'exé uter aussie a ement à un oût bieninférieur. Nouspensonsque e travail sera utile pourbeau oupd'appli ations P2P,pour lesquellesilaétémontréque hoisir sespartenaires,en sebasant surleur disponibilité, améliore de façon onséquenteles performan es dusystème.
1. Introdu tion
Churnisoneofthemost riti al hara teristi sofpeer-to-peer(P2P)networks,asthepermanent owofpeer onne tionsanddis onne tions anseriouslyhamperthee ien yofappli ations[9 ℄. Fortunately,ithasbeen shownthat, formanypeers,theseeventsgloballyobeysome availability patterns([19,20, 2℄), andso, an be predi tedfromthe uptimehistoryof those peers [15℄. To take advantage of these predi tions, appli ations need to be able to dynami ally nd good partnersfor peers,a ordingto these availability patterns,eveninlarge-s ale unstru tured net-works. Theintrinsi onstitution ofthose networksmakespurerandom mat hingte hniques to betime-ine ient fa ing hurn.
Inthis paper, westudy ageneri te hnique to usesu hpartners, andapply itfortwo parti ular mat hingproblems: dis onne tion mat hing ,where peers lookfor partners expe tedto dis on-ne t at the same time, and presen e mat hing, where peers look for partners expe ted to be online simultaneouslyinthefuture. Theseproblems arespe i ed inSe tion 2.
We then propose to use standard epidemi proto ols for topology management to solve these problems. However, inorderto onverge to the desiredstate or topology (here mat hed peers),
Mat hing: peer
y
is a bet-ter mat h than peerz
for peerx
.su h proto ols require good metri s to ompute the distan ebetween peers. Thesemetri s and a well knownepidemi proto ol, T-Man[12 ℄, aredes ribed inSe tion 3.
Toevaluatethee ien yofourproposal,wesimulatedanappli ationforea hmat hingproblem: an appli ation of task s heduling, where tasks of multiple remote jobs are started by all the peers in the network (dis onne tion mat hing), and an appli ation of P2P le-system, where peers repli ate les on other peers to make them highly available (presen e mat hing). These appli ationsare spe i edinSe tion 5.
Torunoursimulationsonarealisti workload,we olle tedanewtra eofpeeravailabilityonthe eDonkey le-sharingnetwork. Withthe onne tionsand dis onne tions of14 millionpeers over 27days,thistra eisthelargestavailableworkload,withdetailedinformationontheavailability of peers. In Se tion 4,we showthatpeers inthis tra e exhibit availability patterns, and,using a simple 7-day predi tor, that it is possible to sele t predi table peers and su essfully predi t their behavior over the following week. The new eDonkey tra e and this simple predi tor are studied inSe tion 4.
Our simulation results showed thatour T-Man based solution is ableto provide good partners toallpeers,forbothappli ations. Usingavailabilitypatterns, bothappli ationsareableto keep the same performan e, while onsuming 30% less resour es, ompared to a random sele tion of partners. Moreover, T-Man is s alable and inexpensive, making the solution usable for any appli ation and network size. Theseresults aredetailedinSe tion 6.
Finally,we brie ypresent some relatedwork inSe tion 7 before on luding inSe tion 8.
2. Problem Spe i ation
This se tion presents two availability mat hing problems,dis onne tion mat hing and presen e mat hing. Ea h problem is abstra ted from the needs of a pra ti al P2P appli ation that we des ribe afterwards. But rst,we start byintrodu ing our systemand network models.
2.1. System and Network Models
We assume a fully- onne ted asyn hronous P2P network of
N
nodes, withN
usually ranging fromthousandstomillionsofnodes. Weassumethatthereisa onstantboundn
c
onthenumber of simultaneous onne tions that a peer an engage in, typi ally mu h smallerthanN
. When peers leave the system, they dis onne t silently. However, we assume that dis onne tions are dete ted after atime∆
disc
,for example30 se onds withTCP keep-alive.For ea h peer
x
, we assume the existen e of an availability predi tionP r
x
(t)
, starting at the urrent time
t
and for a periodT
in the future, su h thatP r
x
(t)
is a set of non-overlapping intervalsduringwhi h
x
isexpe tedtobeonline. Thesepredi tionsare omputed onthehistory ofavailabilityprovided byx
. Inthepresen eofmali iouspeers,se ure proto olsfor availability measurement [16, 14℄mustbeused to he kthatx
is not lyingon itshistory.We note
S
P r
x
(t)
the set de ned by the union of the intervals of
P r
x
(t)
, and
||S||
the size ( ardinal) ofa setS
.peer
y
isabettermat hthanpeerz
for peerx
.2.2. The Problemof Dis onne tion Mat hing
Intuitively, theproblemof Dis onne tion Mat hing is, for a peeronline at a given time, to nd a setofother online peers whoare expe tedto dis onne t at thesametime.
Formally, for a peer
x
online at timet
, an online peery
is a better mat h for Dis onne tion Mat hing than an online peerz
if|t
x
− t
y
| < |t
x
− t
z
|
,where[t, t
x
[∈ P r
x
(t)
,[t, t
y
[∈ P r
y
(t)
and[t, t
z
[∈ P r
z
(t)
. TheproblemofDis onne tionMat hing
DM (n)
istodis overthen
bestmat hes ofonline peers atanytime.The problem of Dis onne tion Mat hing typi ally arises in appli ations where a peer tries to nd partnerswith whom it wants to ollaborate until theend of its session, inparti ular when starting su ha ollaboration mightbe expensive intermsof resour es.
Anexampleofsu hanappli ationistasks hedulinginP2Pnetworks. InZorilla[7℄forexample, a peer an submita omputation taskof
n
jobsto the system. In su h a ase, the peertries to lo aten
online peers(withexpandingringsear h) tobe ome partnersfor thetask,andexe utes then
jobsonthesepartners. Whenthe omputationisover,thepeer olle ts then
resultsfrom then
partners. WithDis onne tion Mat hing, su h a systembe omes mu h more e ient: by hoosingpartnerswhoarelikelytodis onne tatthesametimeasthepeer,thesystemin reases theprobabilitythat:•
If the peer does not dis onne t too early, its partners will have time to nish exe uting their jobsbefore dis onne tingand itwill be ableto olle t theresults;•
Ifthe peer dis onne ts beforethe end ofthe omputation,partners will not waste unne -essaryresour es asthey arealso likelyto dis onne t at thesame time.2.3. The Problemof Presen e Mat hing
Intuitively, theproblemof Presen e Mat hingis, for a peer online at agiven time, to nd aset ofother online peerswhoareexpe tedto be onne ted at thesame timeinthefuture.
Formally, for a peer
x
online at timet
,an online peery
is a better mat h for Unfair Presen e Mat hingthan anonline peerz
if:||
[
P r
z
(t) ∩
[
P r
x
(t)|| < ||
[
P r
y
(t) ∩
[
P r
x
(t)||
This problemis alled unfair,sin e peers who are always online appear to be bestmat hes for all other peers in the system, whereas only other always-on peers are best mat hes for them. Sin e some fairness is wanted in most P2P systems, o ine periods should also be onsidered. Consequently,
y
isa bettermat h thanz
for Presen e Mat hingif:||
S
P r
z
(t) ∩
S
P r
x
(t)||
||
S
P r
z
(t) ∪
S
P r
x
(t)|
<
||
S
P r
y
(t) ∩
S
P r
x
(t)||
||
S
P r
y
(t) ∪
S
P r
x
(t)||
The problemof Presen e Mat hing
P M (n)
is to dis over then
best mat hes of online peers at anytime.The problem of presen e mat hing arises in appli ations where a peer wants to nd partners that will be available at the same time inother sessions. This is typi ally the ase when huge
thatdata.
An example of su h an appli ation is storage of les in P2P networks [4, 6, 17 ℄. For example, inPasti he [6 ℄, ea h peerin the system hasto nd other peers to store its les. Sin e les an only be used when the peer is online, the best partners for a peer (at equivalent stability) are thepeerswhoare expe tedto beonline when thepeer itselfisonline.
Moreover,inaP2Pba kupsystem[8℄,peersusuallyrepla etherepli athat annotbe onne ted for a given period, to maintain a given level of data redundan y. Using presen e mat hing, su happli ations an in reasetheprobabilityofbeingableto onne tto alltheirpartners, thus redu ing their maintenan e ost.
3. Uptime Mat hing with Epidemi Proto ols
Wethink thatepidemi proto ols[21 , 22,13 ℄aregoodapproximate solutionsfor thesemat hing problems. Here, we present one of these proto ols, T-Man[12 ℄ and, sin e su h proto ols rely heavilyonappropriatemetri s,weproposetwodierentmetri s,oneforea hmat hingproblem. 3.1. Distributed Mat hing with T-Man
T-Man is a well-known epidemi proto ol, usually used to asso iate ea h peer in the network withasetofgoodpartners, givenametri (distan efun tion)betweenpeers. Eveninlarge-s ale networks, T-Man onverges fast, and provides a good approximationof the optimal solution in a fewrounds, where ea h round ostsonlyfour messagesinaverageperpeer.
In T-Man, ea h peer maintains two small sets, its random viewand its metri view, whi h are, respe tively,some randomneighbors,andthe urrent best andidatesfor partnership,a ording to themetri inuse. During ea hround,everypeerupdates itsviews: withone randompeerin its randomview,it mergesthe two randomviews, and keepsthemost re ently seenpeers inits random view;with the bestpeerin itsmetri view, itmerges all theviews, and keeps only the bestpeers, a ordingto the metri ,initsmetri view.
This double s heme guarantees a permanent shu e of the random views, while ensuring fast onvergen eofthemetri viewstowardstheoptimalsolution. Consequently,the hoi eofagood metri is very important. We propose su h metri s for the two availability mat hing problems inthenext part.
3.2. Metri s for Availability Mat hing
To ompute e iently the distan e between peers, the predi tion
P r
x
(t)
is approximated by a bitmap of size
m
,pred
x
, where entry
pred
x
[i]
is 1 if
[i × T /m, (i + 1) × T /m[
is in luded in an interval ofP r
x
(t)
for
0 ≤ i < m
. Note that these metri s an be used with any epidemi proto ol, not only withT-Man.3.2.1. Dis onne tion Mat hing
The metri omputes thetimebetween thedis onne tions oftwo peers. In ase ofequality, the PM-distan e of3.2.2 is usedto preferpeerswiththesame availabilityperiods:
DM-distan e
(x, y) = |I
x
− I
y
|+
PM-distan e
(x, y)
where0
100000
200000
300000
400000
500000
600000
0
5
10
15
20
25
30
Number of Peers
Days
Global System Availability
Online Peers
Figure3: Diurnalpatternsare learly vis-ible when we plot the number of online peers at any time in our 27-day eDon-key tra e. Dependingon thetime of the day, between 300,000 and 600,000 users are onne tedto asingleeDonkeyserver.
3.2.2. Presen e Mat hing
Themetri rst omputestheratioof o-availability(timewherebothpeersweresimultaneously online)ontotal availability (timewhereat leastonepeerwasonline). Sin ethedistan eshould be lose to 0 whenpeersare lose, we thenreverse thevalueon [0,1℄:
PM-distan e
(x, y) = 1 −
P
0
≤i<m
min(pred
x
[i],pred
y
[i])
P
0
≤i<m
max(pred
x
[i],pred
y
[i])
Notethat, while the PM-distan evalueis in[0,1℄, theDM-distan evalue isin[0,m℄.
4. Simulation Settings
WeevaluatedourasolutionbasedonT-Manontwoappli ations,oneforea hmat hingproblem. Inthisse tion,wedes ribeoursimulationsettings. Inparti ular,we des ribethe hara teristi s of the tra e we olle ted for theneeds ofthis study, withmore than 300,000 online peers on 27 days. With a few thousand peers online at the same time, most other tra es olle ted on P2P systems[19,10,2℄la kmassive onne tionanddis onne tiontrends,for thestudyofavailability patternson alarge s ale.
4.1. A new eDonkey Tra e
In 2007, we olle ted the onne tion and dis onne tion events fromthe logs of one of themain eDonkeyserversinEurope. Edonkey is urrently themost usedP2P le-sharingnetwork inthe world. Ourtra e,availableonourwebsite[1℄, ontains morethan200millionsof onne tionsby more than 14 millions of peers,overa period of 27 days. To analyse this tra e,we rst ltered useless onne tions (shorter than 10 minutes) and suspi iousones (too repetitive,simultaneous or with hangingidenti ers), leading to a ltered tra e of 12 millionpeers.
The numberofpeers online at thesame timeinthe lteredtra e is usuallymore than 300,000, asshown by Fig.3. Global diurnal patternsof around 100,000 users arealso learly visible: as shown by previous studies [11 ℄, most eDonkey users are lo ated inEurope, and so, their daily o ine periods areonly partially ompensated by onne tions fromother ontinents.
For everypeerinthe lteredtra e,the auto- orrelation onitsavailabilityperiodswas omputed on14days,withastepofoneminute. Foragivenpeer,theperiodforwhi htheauto- orrelation is maximum gives its best pattern size. The number of peers with a given best pattern size is plotted onFig.4,andshows,as ouldbeexpe ted,thatthebestpatternsizeisaday,andmu h further,a week.
1000
10000
100000
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14
Number of peers (log scale)
Best pattern size (days)
Distribution of the Best Sizes of Patterns
Figure4: For ea h peer, we omputed the auto orrelation (ressemblan e) of its availability bitmap for dierent osets. We then omputed and plotted for ea h peer the oset (best pattern size) lead-ingtothemaximalauto- orrelation(best ressemblan e). Most peers a hieve their bestauto- orrelationforanoset loseto one day or one week: peers are highly likely to onne tatalmostthesame time thenext dayor thenext week.
4.2. Filtering and Predi tion
Ourgoalinthesesimulationswastoevaluatethee ien y ofourmat hingproto ol,andnotthe e ien y ofavailabilitypredi tors,asalreadydonein[15 ℄. Asa onsequen e,weimplementeda very straightforward predi tor, that uses a 7-daywindow of availability history to ompute the daily pattern of a peer: for ea h intervalof 10 minutes ina day,its valueis thenumber of days intheweek where the peer wasavailable duringthatfull interval:
pattern
p
[i] = Σ
d∈[0:6]
history
p
[d ∗ 24 ∗ 60/10 + i]
Thispredi tor hastwo purposes:
•
Itshouldhelptheappli ationto de idewhi hpeers arepredi table,and thus,whi h peers an bene t from an improved quality of servi e. This gives an in entive for peers to parti ipateregularlyto thesystem;•
it should help the appli ation to predi t future onne tions and dis onne tions of the sele ted peers.To sele t predi table peers,thepredi tor omputes, for ea h peer, themaximumand themean ovarian eofthepeerdailypattern. Forthesesimulations, we omputedaset, alledpredi table set, ontaining peers mat hing withthe following properties:
•
The maximum value inpattern
is at least 5: ea h peer was available at least ve days duringthelast week exa tlyat thesame time;•
The average ovarian e inpattern
is greater than 28: ea h peer has a sharply-shaped behavior;•
Peer availability isgreaterthan 0.1: peershave to ontribute enough to thesystem;•
Peer availability is smaller than 0.9: peers whi h are always online would bias positively our simulations.Inour eDonkeytra e,this predi table set ontains 19,600 su h peers. For everypeerintheset, thepredi tor predi ts that thepeerwill beonline ina given interval ifthepeer'sdaily pattern valueforthatintervalisat least5,and otherwisepredi tsnothing(wenever predi tthatapeer will be o ine).
0
0.2
0.4
0.6
0.8
1
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Prediction Success
Availability
CDF of Peers (normalized)
Predictability of selected peers
prediction (predictable peers)
prediction (randomized bitmaps)
Availability
availability bitmap of the rst week to predi t its availability during these ond week. We omputed the su ess rate on the bitmap of the se ond week, or a randomized bitmap with similar avail-ability. While availability determines the predi tion su ess with randomized bitmaps, dailypatterns improve the pre-di tion with real bitmaps (e.g. for 40% of peers (x
≥
0.6),more than 60%of the predi tions (y≥
0.6) are su essful, but only 30%withrandomized bitmaps).Figure5showsthatpredi tions annotbeonlyexplainedbya identalavailability,andprovesthe presen eof availability patternsinthetra e. The gureplots theratio of su essfulpredi tions afteraweekfor thefull following week. For ea hpeerinthepredi table set, weusedits bitmap of availabilityon the rst week of thetra e to ompute its predi tedavailability for these ond week. We then ompared the predi tion with thereal bitmap observed on the se ond week, to obtain the predi tion su ess rate. However, even in theabsen e of availability patterns, there is a non-null probability of su ess when predi ting thata peer is online, mostlydepending on its availability. To take this probability into a ount, we omputed a randomized bitmap of the se ond week for ea h peer, i.e. a bitmap with the same availability where patterns have been deleted by randomization. As expe ted, we were more su essful at predi ting the real bitmap than the randomized one, therefore proving the existen e of availability patterns, and the probability of su ess is lose to the peer availability for randomized bitmaps, i.e. without availabilitypatterns.
We purposely hose a very simple predi tor, as we are interested in showing that patterns of presen e are visible and an bene t appli ations, even with a worst- ase approa h. Therefore, we expe t that better results would be a hieved using more sophisti ated predi tors, su h as des ribed in[15℄,and for anoptimal pattern size ofone dayinsteadofa week.
4.3. General Simulation Setup
A simulator was developed from s rat h to run the simulations on a Linux3.2 GHz Xeon om-puter, for the 19,600 peers of the predi table set from Se tion 4.2. Theirbehaviors on 14-days wereextra ted fromthe eDonkeytra e: the rst7 days wereusedto ompute apredi tion,and thatpredi tion, withoutupdates,wasusedto exe utetheproto olon thefollowing seven days. During oneround of thesimulator, allonline peers inrandomorderevaluate one T-Manround, orresponding to one minute of the tra e. As explained later, both appli ations were delayed by a period of 10 minutes after a peer would ome online to allow T-Man to provide a useful metri view. The omputationofa ompleterun didnot ex eedtwo hoursand 6GBofmemory footprint.
5. Simulated Appli ations
Inthisse tion,wedes ribethetwoappli ationsthatweusedtoillustratetheneedforane ient proto ol for distributed availability mat hing. Our goal is not to improve the performan e of
0
5000
10000
15000
20000
25000
30000
UptimeRandom
UptimeRandom
UptimeRandom
Number of Tasks
Impact of Disconnection Matching for P2P scheduling
Completed Tasks
Aborted Tasks
Week Mean
Day +7
Day + 1
Figure6: A taskis a set of three remote jobsof4hoursstartedbyevery peer, ten minutes after oming online. A task is su essfulwhenthepeeranditspartners arestillonlineafter4hoursto olle tthe results. Using availability predi tions, a peer an de ide not to start a task ex-pe tedtoabort,leading tofeweraborted tasks. Using dis onne tion mat hing, it an nd good partners and it an still omplete almost as many tasks as the mu hmore expensive randomstrategy.
these appli ations, asthis an bedone byanaggressive greedy algorithm,but to save resour es using availability information.
5.1. Dis onne tion Mat hing: Task S heduling
Toevaluatethee ien yofT-ManandtheDM-distan emetri ,wesimulatedadistributedtask s heduling appli ation. In this appli ation, every peer starts a task after 10 minutes online: a task is omposed of 3 jobs of 4 hours on remote partners, and is ompleted if the peer and its partnersarestill online after4 hoursto olle t the results.
The2 rsthoursofea hjobaredevotedtothedownloadofthedataneededforthe omputation from a entral server. As a onsequen e, a peer an de ide not to start a task to save the bandwidthof the entral server. In oursimulation, su ha de isionis taken whenthepredi tion ofthe peeravailabilityshowsthatthe peerisgoing to goo ine before ompletion of thetask. 5.2. Presen e Mat hing: P2P File-Storage
Toevaluatethee ien yofT-ManandthePM-distan emetri ,wesimulated aP2P lestorage appli ation. In this appli ation, every peerrepli ates its data to its partners, tenminutes after oming onlinefor the rst time,inthe hopethatitwillbeableto usethis remotedatathenext timeitwill beonline.
Thesize of thedataofea h peer issupposedto be large,hundredofmegabytesof example. As a onsequen e, it isimportant for thesystem to use aslittle redundan y aspossible to a hieve high o-availability of data (i.e. availability of the peer and at least one of its data repli a). Findinggoodpartnersinthenetwork isexpe tedto provide repli a whi haremore likely to be available at thesame timeasthepeer, thus de reasingthe need for more repli as.
6. Simulation Results
In this se tion, we present the results of our simulations of the two appli ations. We are not interestedintherawperforman eoftheseappli ations,butinthesavingsthat ouldbea hieved byusingavailabilityinformation and partner mat hing.
6.1. Results for Dis onne tion Mat hing
We omparedDis onne tionMat hingwithaRandom hoi eofpartners(a tually,usingpartners within T-Man random view) for the distributed task s heduling appli ation. The number of ompletedtasks andthe numberofabortedtasksareplotted onFig.6,for the rstday,the7
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Uptime
Random
Uptime
Random
Uptime
Random
Co-Availability
Impact of Presence Matching for P2P File Storage
1 repl
2 repl
3 repl
4 repl
5 repl
6 repl
7 repl
8 repl
9 repl
Week
Day + 7
Day + 1
Figure7: 10 minutes after oming on-linefor the rsttime,ea h peer reatesa given number of repli a for its data. Co-availability is de ned by the simultane-ouspresen e ofthepeerand at leastone repli a. Using presen e mat hing, fewer repli as are needed to a hieve better re-sultsthanusing arandom hoi eof part-ners. Even the 7th day, using a 6-day old predi tion, the system still performs mu hmoree iently,almost ompensat-ingthegeneral lossinavailability.
dayandthewhole week.
Predi tionof availabilityde reasedby68%the numberofabortedtasksonaverageoveraweek, orresponding to 50%of bandwidth savingson thedata server, whilede reasing the number of ompleted tasksbyonly17%.
These results were largely improved using one-day predi tion, sin e one-week predi tion is ex-pe tedto belessa urate (see auto- orrelation inSe tion 4.1). Indeed,bandwidthsavingswere about 43% for Dis onne tion Mat hing, while ompleting 20% more tasks. Thus, it is mu h more interesting froma performan e point of view to use one-day predi tion every day instead ofone-week predi tion,although savingsare stillpossible with one-week predi tions.
6.2. Results for Presen e Mat hing
We ompared Presen e Mat hing with a Random hoi e of repli a lo ations for the P2P le-systemappli ation. The o-availability of thepeer and at leastone repli a isplotted on Fig. 7, for dierent numberof repli as.
Usingpresen emat hing,fewerrepli aswereneededtoa hievebetterresultsthanusingarandom hoi e ofpartners. For example,1 repli awith Presen eMat hinggives abetter o-availability than 2repli as withRandom Choi e;5repli as withPresen eMat hinggivea o-availabilityof 95%whi h isonly a hieved using9 repli as withRandomChoi e. As forthe otherappli ation, week-old predi tionsperformedstill better than random hoi e inthesame orders.
7. Related Work
We believe that many P2P systems and appli ations an bene t from this work, as a lot of availability-awareappli ationshave been proposedintheliterature[3,8 ,18,5,23 ℄. Closeto our work,[9℄showsthatstrategiesbasedonthelongest urrentuptimearemoree ientthan uptime-agnosti strategiesforrepli apla ement; [15℄introdu essophisti atedavailabilitypredi torsand showsthatthey an beverysu essful. However, tothebestof ourknowledge, thispaperisthe rstto dealwiththe problemof ndingthebest partnersa ordingtoavailabilitypatternsina large-s ale network. Moreover,previous results areoften omputed onsyntheti tra esor small tra esof P2Pnetworks.
In this paper, we showed that epidemi proto ols for topology management an be e ient to nd good partners in availability-aware networks. Simulations proved that, using one of these proto olsandappropriatemetri s,su happli ations anbelessexpensiveandstillperform with anequivalentorbetterqualityofservi e. Weusedaworst- ases enario: asimplepredi tor,and a tra e olle ted from a highlyvolatile le-sharingnetwork, where only a small subset of peers provide predi table behaviors. Consequently, weexpe tthata real appli ation wouldtake even more bene tfrom availabilitymat hingproto ols.
Inparti ular,until thiswork,availability-awareappli ationswerelimitedtousingpredi tionsor availabilityinformation to better hooseamonga limitedsetof neighbors. Thiswork opensthe door to new availability-aware appli ations, where best partners are hosenamong all available peersinthenetwork. Itisauseful omplementtotheworkdoneonmeasuringavailability[16,14℄ and usingthese measures to predi tfutureavailability[15℄.
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